Marietta College

Marietta College
Spring 2011 Econ 420: Applied Regression Analysis Dr. Jacqueline Khorassani Week 12

Tuesday, March 29 Exam 3: Monday, April 25, 12- 2:30PM

The 2011-2012Fitzgerald Executive-in-Residence Project Focus Employee Satisfaction in the Workplace Leader Dale Wartluft’63, a retired senior executive and member of the Marietta College Board of Trustees Two teams of students focus on two companies Send application due electronically to Dr. Gama Perruci (perrucig@marietta.edu) by Monday, April 11 I have posted program information and application form on my website

LeadershipQ&A Cosponsored by McDonough Center for Leadership & Business and the Economic Roundtable of the Ohio Valley Tuesday April 5 7:30pm McDonough Gallery Topic: “How Do We Grow From Here? The Post-Crisis American Economy” David LeonhardtEconomics Journalist Washington Bureau The New York Times

This is the last bonus opportunity of this semester 2 points for attending 2-5 points per question 2-10 points per summary Summaries are due before 5 pm on Friday, April 8 via an email attachment to me Total bonus points will be divided by 3 and added to your exams.

Intercept Dummies Theory 1: Men, in general, earn more than women How do we formulate a model to capture this difference?

Graph of earnings versus experience Earnings Male Female Years of work

How would a dummy variable capture this? Intercept dummy Earnings = β0 + β1 (gender) + β2 (years of work) + error Where gender is dummy variable that takes a value of 1 if the observation is a male and 0 otherwise.

So you add one more variable to your data set. Suppose you have 5 observations in your data set, then it will look like this

Testing the theory Say you estimate your model as usual and get Earnings^ = 1000+ 200 (gender) + 500(years of work) How do you set up hypotheses to test the theory? H0: β1 ≤0 Ha: β1>0 If you reject H0, then you have found significant evidence that men, in general earn more than women

How much more? If your observation is a male Earnings^ = 1000+ 200 (1) + 500(years of work) Earnings^ = 1200+ 500(years of work) If your observation is female Earnings^ = 1000+ 200 (0) + 500(years of work) Earnings^ = 1000+ 500(years of work)

Graph of earnings versus experience Earnings hat Male 1200 Female 1000 Years of work

Slope Dummies Theory 2: Men’s earnings grow at a higher rate than women’s earnings

Graph of earnings versus experience Earnings Male Female Years of work

How would a dummy variable capture this? Slope dummy Earnings = β0 + β1 (years of work) + β2 (years of work) *( gender) + error Where gender is dummy variable that takes a value of 1 if the observation is a male and 0 otherwise.

Suppose you have 5 observations in your data set, you will generate a new variable (Genwork). Genwork is gender times years of work. your data set will look like this GENWORK is called an interactive variable

Testing the theory Let’s say you estimate your model as usual and get Earnings^ = 1000+ 500(years of work) +70 (Genwork) How do you set up the hypotheses to test the theory? H0: β2 ≤0 Ha: β2>0 If you reject H0, then you have found significant evidence that men’s earnings grow at a higher rate with years of experience.

How much more? If your observation is a male Earnings^ = 1000+ 500(years of work) + 70 (years of work)* (1) Earnings^ = 1200+ 570(years of work) If your observation is female Earnings^ = 1000+ 500(years of work) + 70 (years of work) * (0) Earnings^ = 1000+ 500(years of work)

Graph of earnings versus experience Earnings Male slope = 570 Female slope = 500 Years of work

What if The theory suggested that not only, in general, men’s salaries are higher than women’s salaries but men also receive a higher rate of increases in their salaries compared to women over time. Then you are better off to estimate the model twice: once for male observations and once for female observations as the slope and the intercept must be allowed to vary across genders.

Asst 17 (in teams-20 minutes) In Chapter 2, open the “FINAID” file Variables are defined on page 43 Male is dummy that takes a value of 1 for male students At 10 percent level of significance test the hypothesis that, in general, male students receive fewer dollars of financial aid than female students. At 10 percent level of significance test the hypothesis that the effect of the amount that the parents of a student are judged to be able to contribute toward college expenses on the amount of financial aid awarded to a student depends on the student’s gender.

Asst 18: Due Thursday # 12 Page 240

Thursday, March 31 Asst 19 due Tuesday # 5 Page 234 Including Part e (data is available online under STOCK in Chapter 7) Also on Tuesday there will be an in class assignment (Asst 20) on Multicollineairty (Chapter 8) Need data set DRUGS (Chapter 5) Exam 3: Monday, April 25, 12- 2:30PM

Collect Asst 18 # 12 Page 240

LeadershipQ&A Cosponsored by McDonough Center for Leadership & Business and the Economic Roundtable of the Ohio Valley Tuesday April 5 7:30pm McDonough Gallery Topic: “How Do We Grow From Here? The Post-Crisis American Economy” David LeonhardtEconomics Journalist Washington Bureau The New York Times

This is the last bonus opportunity of this semester 2 points for attending 2-5 points per question 2-10 points per summary Summaries are due before 5 pm on Friday, April 8 via an email attachment to me Total bonus points will be divided by 3 and added to your exams.

Return and discuss Asst 17 In Chapter 2, open the “FINAID” file Variables are defined on page 43 Male is dummy that takes a value of 1 for male students At 10 percent level of significance test the hypothesis that, in general, male students receive fewer dollars of financial aid than female students. At 10 percent level of significance test the hypothesis that the effect of the amount that the parents of a student are judged to be able to contribute toward college expenses on the amount of financial aid awarded to a student depends on the student’s gender.

At 10 percent level of significance test the hypothesis that, in general, male students receive fewer dollars of financial aid than female students. Included observations: 50 Dependent Variable: FINAID Variable Coefficient Std. Error t-Statistic Prob. C 9813.022 1743.100 5.629638 0.0000 HSRANK 83.26124 20.14795 4.132492 0.0002 PARENT -0.342754 0.031505 -10.87921 0.0000 MALE -1570.143 784.2971 -2.001975 0.0512 Coefficient of MALE is negative and significant at 10% Let’s see the graph of FINAID against PARENT holding HSRANK constant

At 10 percent level of significance test the hypothesis that the effect of the amount that the parents of a student are judged to be able to contribute toward college expenses on the amount of financial aid awarded to a student depends on the student’s gender. Dependent Variable: FINAID Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 8741.326 1659.361 5.267887 0.0000 HSRANK 91.13511 19.76721 4.610418 0.0000 PARENT -0.308050 0.036411 -8.460356 0.0000 MALEPAR -0.103247 0.043104 -2.395285 0.0207 Coefficient of MALEPAR is different from zero at 10% Let’s see the graph of FINAID against PARENT holding HSRANK constant

Let’s look at the Phillips Curve in economics Inflation % The Phillips Curve shows an inverse relationship between inflation and unemployment. 2.5% 1.5% 4% 6% Unemployment (%) PC

How do we formulate the model? How about Y = β0 + β1 X+ є ? Where Y is inflation and X is unemployment No, the line is non-linear Y = β0 + β1 (1/ X) + є Or Y = β0 + β1 X-1 + є What is the slope of a line showing the relationship between Y an X? dY/dX = - β1 X-2, or dY/dX = (- β1)* 1/ X2 Do we expect β1 to be positive or negative? Positive Note that as X goes up slope declines

Sometimes the theory suggests that when X is changed this period, Y is expected to change next period. Can you think of an example? How do we formulate the model? How do you test the theory? What is the meaning of the estimated coefficient?

3 problems with non-linear models Hard to interpret the meaning of the estimated coefficients Slope? Increasing at a declining rate or increasing at an increasing rate? Policy implications? Elasticity? Neither slope nor elasticity? The adjusted R squared can be compared across two equations only if the dependent variables are the same. An incorrect function may be a good fit for sample observations but not for population observations

Perfect Multicollinearity (Chapter 8) When two or more independent variables have a perfect (error free) linear relationship with each other Which assumption does this violate? (Page 94) Violates Assumption 6 Example Unemployment = f (nominal interest, real interest, inflation) Consequences: OLS is not able to estimate the model Remedy? Drop one variable

Imperfect Multicollinearity When two or more independent variables have an imperfect linear relationship with each other Example Price of a house = f (number of bedrooms, square footage)

Consequences of Imperfect Multicollinearity β hats are unbiased β hats have higher than normal variance Increases the chances of getting a β hat that has the unexpected sign β hats have higher than normal standard errors What does this imply with regards to t- test? Lower t-stats We may conclude that βs are not significantly different from zero while they are significantly different from zero. Adding and subtracting variables and observations will affect βhats significantly The adjusted R squared remains largely unaffected The βhats of uncorrelated variables remain unaffected

Informal detection of Multicollinearity If you have high adjusted R squared but low t-stats suspect a multicollinearity problem

Formal test for Multicollinearity Calculate the correlation coefficients (r) between each pair of independent variables and each independent variable and the dependent variable. EViews direction: quick  group statistics correlation type your variables (starting with your dependent variable… no need for constant) Two rules 1) If |rX1, X2|> |rX1, Y |  problem, or 2) If |rX1, X2 |> 0.8 problem

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